基于混合偏移正交多项式和块脉冲函数的数值方法求解分式微分方程系统

IF 1.7 4区 工程技术 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Complexity Pub Date : 2024-07-09 DOI:10.1155/2024/6302827
Abdulqawi A. M. Rageh, Adel R. Hadhoud
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引用次数: 0

摘要

本文基于具有广义块脉冲函数的混合移位正交伯恩斯坦多项式(HSOBBPFs)和具有广义块脉冲函数的混合移位正交列根德多项式(HSOLBPFs),开发了两种求解分数微分方程系的数值方法。利用这些混合基和运算矩阵方法,分数微分方程系被简化为代数方程系。我们进行了误差分析,并提供了一些仿真实例来证明所提技术的有效性。建议方法的数值结果与现有数值方法的结果进行了比较。这些方法的显著特点是能够在较宽的区间 [0, a]内工作,而且精度高、收敛快,这表明所提出的方法比其他数值方法更有用。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

Numerical Methods Based on the Hybrid Shifted Orthonormal Polynomials and Block-Pulse Functions for Solving a System of Fractional Differential Equations

Numerical Methods Based on the Hybrid Shifted Orthonormal Polynomials and Block-Pulse Functions for Solving a System of Fractional Differential Equations

This paper develops two numerical methods for solving a system of fractional differential equations based on hybrid shifted orthonormal Bernstein polynomials with generalized block-pulse functions (HSOBBPFs) and hybrid shifted orthonormal Legendre polynomials with generalized block-pulse functions (HSOLBPFs). Using these hybrid bases and the operational matrices method, the system of fractional differential equations is reduced to a system of algebraic equations. Error analysis is performed and some simulation examples are provided to demonstrate the efficacy of the proposed techniques. The numerical results of the proposed methods are compared to those of the existing numerical methods. These approaches are distinguished by their ability to work on the wide interval [0, a], as well as their high accuracy and rapid convergence, demonstrating the utility of the proposed approaches over other numerical methods.

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来源期刊
Complexity
Complexity 综合性期刊-数学跨学科应用
CiteScore
5.80
自引率
4.30%
发文量
595
审稿时长
>12 weeks
期刊介绍: Complexity is a cross-disciplinary journal focusing on the rapidly expanding science of complex adaptive systems. The purpose of the journal is to advance the science of complexity. Articles may deal with such methodological themes as chaos, genetic algorithms, cellular automata, neural networks, and evolutionary game theory. Papers treating applications in any area of natural science or human endeavor are welcome, and especially encouraged are papers integrating conceptual themes and applications that cross traditional disciplinary boundaries. Complexity is not meant to serve as a forum for speculation and vague analogies between words like “chaos,” “self-organization,” and “emergence” that are often used in completely different ways in science and in daily life.
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